C suryanarayana, m grant norton (auth ) x ra(bookzz org)

X-Ray Diffraction A Practical Approach X-Ray Diffraction A Practical Approach c Suryanarayana Colorado School of Mines Golden, Colorado and M Grant Norton Washington State University Pullman, Washington Springer Science+Business Media, LLC Library of Congress Cataloging in Publication Data On file ISBN 978-1-4899-0150-7 DOI 10.1007/978-1-4899-0148-4 ISBN 978-1-4899-0148-4 (eBook) © 9 Springer Science+Business Media New York Originally published by Plenum Publishing Corporation in 1998 Softcover reprint of the hardcover 1st edition 1998 10987654321 All rights reserved N o part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher Preface X-ray diffraction is an extremely important technique in the field of materials characterization to obtain information on an atomic scale from both crystalline and noncrystalline (amorphous) materials The discovery of x-ray diffraction by crystals in 1912 (by Max von Laue) and its immediate application to structure determination in 1913 (by W Bragg and his father W H Bragg) paved the way for successful utilization of this technique to determine crystal structures of metals and alloys, minerals, inorganic compounds, polymers, and organic materials-in fact, all crystalline materials Subsequently, the technique of x-ray diffraction was also applied to derive information on the fine structure of materials-crystallite size, lattice strain, chemical composition, state of ordering, etc Of the numerous available books on x-ray diffraction, most treat the subject on a theoretical basis Thus, even though you may learn the physics of x-ray diffraction (if you don't get bogged down by the mathematical treatment in some cases), you may have little understanding of how to record an x-ray diffraction pattern and how to derive useful information from it Thus, the primary aim of this book is to enable students to understand the practical aspects of the technique, analyze x-ray diffraction patterns from a variety of materials under different conditions, and to get the maximum possible information from the diffraction patterns By doing the experiments using the procedures described herein and follOwing the methods suggested for doing the calculations, you will develop a dear understanding of the subject matter and appreciate how the information obtained can be interpreted v vi Preface The book is divided into two parts: Part I-Basics and Part II-Experimental Modules Part I covers the fundamental prindples necessary to understand the phenomenon of x-ray diffraction Chapter presents the general background to x-ray diffraction: What are x-rays? How are they produced? How are they diffracted? Chapter reviews the concepts of different types of crystal structures adopted by materials Additionally, the phenomena of diffraction of x-rays by crystalline materials, concepts of structure factor, and selection rules for the observance (or absence) of reflections are explained Chapter presents an overview of the experimental considerations involved in obtaining useful x-ray diffraction patterns and a brief introduction to the interpretation and significance of x-ray diffraction patterns Even though the theoretical aspects are discussed in Part I, we have adopted an approach quite different from that of other textbooks in that we lay more emphasis on the physical significance of the phenomenon and concepts rather than burden you with heavy mathematics We have used boxed text to further explain some particular, or possibly confusing, aspects Part II contains eight experimental modules Each module covers one topic For example, the first module explains how an x-ray diffraction pattern obtained from a cubic material can be indexed First we go through the necessary theory, using the minimum amount of mathematics Then we a worked example based on actual experimental data we have obtained; this is followed by an experiment for you to Finally we have included a few exerdses based on the content of the module These give you a chance to apply further some of the knowledge you have acquired Each experimental module follows a similar format We have also made each module self-contained; so you can work through them in any order, however, we suggest you Experimental Module first since this provides a lot of important background information which you may find useful when you work through some of the later modules By working through the modules, or at least a selection of them, you will discover what information can be obtained by x-ray diffraction and, more importantly, how to interpret that information Work tables have been provided so that you can tabulate your data and results Further, we have taken examples from all categories of materials-metals, ceramics, semiconductors, and polymers-to emphasize that x-ray diffraction can be effectively and elegantly used to characterize any type of material This is an important feature of our approach Another important feature of the book is that it provides x-ray diffraction patterns for all the experiments and lists the values of the Bragg angles (diffraction angles, 0) Therefore, even if you have no access to an Preface x-ray diffractometer, or if the unit is down, you can use these 29 values and perform the calculations Alternatively, if you are able to record the x-ray diffraction patterns, the patterns provided in the book can be used as a reference; you can compare the pattern you recorded against what is given in the book This book is primarily intended for use by undergraduate junior or senior-level students majoring in materials sdence or metallurgy However, the book can also be used very effectively by undergraduate students of geology, physics, chemistry, or any other physical sdence likely to use the technique of x-ray diffraction for materials characterization Preliminary knowledge of freshman physics and simple ideas of crystallography will be useful but not essential because these have been explained in easy-to-understand terms in Part I The eight modules in Part II can be easily completed in a one-semester course on x-ray diffraction If x-ray diffraction forms only a part of a broader course on materials characterization, then not all the modules need to be completed We realize that we have not included all possible applications of x-ray diffraction to materials The book deals only with polycrystalline materials (mostly powders) We are aware that there are other important applications of x-ray diffraction to polycrystalline materials Since this book is intended for an undergraduate course, and some spedal and advanced topics are not covered in most undergraduate programs, we have not discussed topics such as stress measurement and texture analysis in polycrystalline materials X-ray diffraction can also be used to obtain structural information about single crystals and their orientation and the structure of noncrystalline (amorphous) materials But this requires use of a slightly different experimental setup or sophisticated software which is not available in most undergraduate laboratories For this reason we have not covered these topics Pullman, WA C Suryanarayana M Grant Norton vii Acknowledgments In writing any book it is unlikely that the authors have worked entirely in isolation without assistance from colleagues and friends We are certainly not exceptions and it is with great pleasure that we acknowledge those people that have contributed, in various ways, to this project We are indebted to Mr Enhong Zhou and Mr Charles Knowles of the University of Idaho for helping to record all the x-ray diffraction patterns in this book Their attention to detail and their flexibility in accommodating our schedule are gratefully appredated The entire manuscript was read by Professor John Hirth, Professor Kelly Miller, and Mr Sreekantham Sreevatsa, and we thank them for their time and effort and their helpful suggestions and comments Dr Frank McClune of the International Centre for Diffraction Data provided us with the latest information from the Powder Diffraction File Dr Vmod Sikka of Oak Ridge National Laboratory generously provided us with an ingot of Cu3Au Simon Bates of Philips Analytical X-Ray, Rick Smith of Osmic, Inc., and David Aloisi of X-Ray Optical Systems, Inc., contributed helpful discussions and information on recent developments in x-ray instrumentation This book was written while one of the authors (CS) was a Visiting Professor at Washington State University in Pullman We are both obliged to Professor Stephen Antolovich, Director of the School of Mechanical and Materials Engineering at Washington State University, for fadlitating our collaboration and for providing an environment wherein we could complete this book And last, but by no means least, we would like to thank our wives Meena and Christine Their presence provides us with an invisible staff that makes the journey easier It is to them that we dedicate this book ix Contents Part I Basics Chapter X-Rays and Diffraction 1.1 1.2 1.3 1.4 X-Rays The Production of X-Rays Diffraction A Very Brief Historical Perspective 14 18 Chapter Lattices and Crystal Structures 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 Types of Solid and Order Point Lattices and the Unit Cell Crystal Systems and Bravais Lattices Crystal Structures 2.4.1 One Atom per Lattice Point 2.4.2 Two Atoms of the Same Kind per Lattice Point 2.4.3 Two Different Atoms per Lattice Point 2.4.4 More than Two Atoms per Lattice Point Notation for Crystal Structures Miller Indices Diffraction from Crystalline Materials- Bragg's Law The Structure Factor Diffraction from Amorphous Materials 21 23 24 27 27 31 36 40 41 43 50 52 60 Chapter Practical Aspects of X-Ray Diffraction 3.1 Geometry of an X-Ray Diffractometer xi 63 xii Contents 3.2 Components of an X-Ray Diffractometer 3.2.1 The X-Ray Source 3.2.2 The Specimen 3.2.3 The Optics 3.2.4 The Detector 3.3 Examination of a Standard X-Ray Diffraction Pattern 3.4 Sources of Information 3.5 X-Ray Safety 3.6 Introduction to the Experimental Modules 65 65 66 68 72 80 85 91 93 Part II Experimental Modules Module Crystal Structure Determination I: Cubic Structures 97 Module Crystal Structure Determination II: Hexagonal Structures 125 Module Precise Lattice Parameter Measurements 153 Module Phase Diagram Determination 167 Module Detection of Long-Range Ordering 193 Module Determination of Crystallite Size and Lattice Strain 207 Module Quantitative Analysis of Powder Mixtures 223 Module Identification of an Unknown Specimen 237 Appendixes Appendix Plane-Spacing Equations and Unit Cell Volumes 251 Appendix Quadratic Forms of Miller Indices for the Cubic System 254 Appendixes APPENDIX 5: MASS ABSORPTION COEFFICIENTS Wp (cm 2/g) AND DENSITIES P (g/cm ) OF SOME SELECTED ELEMENTS Absorber Atomic Number iI: II C N Na Mg Al Si Cl Ca n Cr Fe Ni Cu Zn Ga Ge As Ag cd Te Cs W Au Po II 12 13 14 17 20 22 24 26 28 29 30 31 32 33 47 48 52 55 74 79 84 Density (g/cm3) 0.08375 x 10-3 0.533 2.27 1.165 X 10-3 1.332 X 10-3 0.966 1.74 2.70 2.33 3.214 x 10-3 1.53 4.51 7.19 7.87 8.91 8.93 7.13 5.91 5.32 5.78 10.50 8.65 6.25 1.91 (-10°e) 19.25 19.28 ILlp Cu Ka ILIP CU Kf} 0.391 0.500 4.51 7.44 II.5 29.7 40.0 49.6 63.7 106 170 200 247 302 48.8 51.8 57.9 62.1 67.9 74.7 213 222 267 317 168 201 254 0.388 0.412 3.33 5.48 8.42 22.0 29.6 36.8 47.5 79.5 129 152 185 232 279 39.2 43.8 47.0 51.4 56.5 163 169 204 243 130 155 196 A=0.154184 run A=0.139222 run The mass absorption coefficients are from International Tables for Crystallography, Volume C, edited by A J C WIlson, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995, pp 200-205 257 258 Appendixes APPENDIX 6: MULTIPLICITY FACTORS Cubic System Miller Indices hkl hhl Ok{ Olck hhh 001 Example Multiplicity 345 48 112 24 012 24 OIl III 002 12 Hexagonal System Miller Indices hkl hhl Okl hkO hhO oka 001 Example Multiplicity 123 24 112 12 012 12 120 12 110 010 6 002 Appendixes APPENDIX 7: LORENTZ-POLARIZATION FACTOR [1 +2 col2a] sin 9° 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 0.0 0.1 0.2 0.3 0.4 0.5 1138 1048 1239 1354 1639 1486 638.8 600.6 565.6 533.6 727.2 680.9 369.9 352.8 336.8 321.9 388.3 408.0 231.4 222.9 214.7 240.5 250.1 260.3 163.1 158.0 153.1 168.5 174.1 180.1 117.6 114.4 128.0 124.4 120.9 131.7 93.03 90.78 88.60 97.80 95.37 100.3 75.31 70.50 73.65 72.05 78.79 77.02 58.46 57.32 62.12 60.86 59.65 63.41 51.06 50.12 49.20 48.30 47.43 52.03 41.20 40.50 39.82 43.39 42.64 41.91 33.85 36.08 35.50 34.94 34.39 36.67 29.08 29.95 29.51 31.34 30.87 30.41 25.56 25.21 27.05 26.66 26.29 25.92 22.32 22.02 23.54 23.23 22.92 22.61 19.38 19.87 19.62 20.64 20.38 20.12 17.15 17.57 17.36 18.00 17.78 18.22 15.80 15.62 15.27 15.45 15.99 16.17 13.66 13.97 13.81 14.44 14.28 14.12 12.67 12.28 12.54 12.41 12.81 12.95 11.31 11.54 11.43 11.66 11.20 11.09 10.34 10.24 10.15 10.05 10.45 10.55 9.400 9.313 9.226 9.141 9.489 9.579 8.730 8.651 8.573 8.496 8.420 8.345 7.984 7.915 7.846 7.778 7.645 7.711 7.205 7.145 7.327 7.265 7.086 7.027 6.691 6.745 6.480 6.637 6.584 6.532 5.995 6.135 6.088 6.041 6.182 6.231 5.564 5.688 5.647 5.605 5.774 5.731 5.292 5.254 5.218 5.181 5.367 5.329 5.006 4.972 4.939 4.906 4.873 4.841 4.685 4.655 4.625 4.595 4.566 4.538 4.399 4.372 4.346 4.320 4.294 4.268 4.145 4.121 4.097 4.074 4.051 4.029 3.919 3.898 3.877 3.857 3.837 3.817 3.720 3.701 3.683 3.665 3.647 3.629 3.544 3.528 3.512 3.495 3.480 3.464 3.361 3.347 3.333 3.320 3.389 3.375 3.242 3.230 3.218 3.206 3.194 3.255 3.117 3.106 3.096 3.086 3.138 3.127 3.038 3.029 3.020 3.011 3.003 2.994 2.954 2.946 2.939 2.932 2.924 2.917 2.884 2.878 2.872 2.866 2.860 2.855 2.828 2.824 2.819 2.814 2.810 2.805 0.6 968.9 504.3 308.0 207.1 148.4 111.4 86.50 68.99 56.20 46.58 39.16 33.33 28.66 24.86 21.74 19.14 16.95 15.10 13.52 12.15 10.98 9.952 9.057 8.271 7.580 6.969 6.429 5.950 5.524 5.146 4.809 4.509 4.243 4.006 3.797 3.612 3.449 3.306 3.183 3.076 2.986 2.911 2.849 2.801 0.7 898.3 477.3 294.9 199.8 144.0 108.5 84.48 67.53 55.11 45.75 38.52 32.81 28.24 24.52 21.46 18.90 16.75 14.93 13.37 12.03 10.87 9.857 8.973 8.198 7.515 6.912 6.379 5.905 5.484 5.110 4.777 4.481 4.218 3.984 3.777 3.594 3.434 3.293 3.171 3.067 2.978 2.904 2.844 2.797 cos 0.9 0.8 835.1 452.4 282.7 192.9 139.7 105.6 82.52 66.11 54.06 44.94 37.88 32.31 27.83 24.19 21.18 18.67 16.56 14.76 13.23 11.90 10.76 9.763 8.891 8.126 7.452 6.856 6.329 5.861 5.445 5.075 4.746 4.453 4.193 3.962 3.758 3.577 3.419 3.280 3.160 3.057 2.970 2.897 2.839 2.793 778.4 429.3 271.1 186.3 135.6 102.9 80.63 64.74 53.03 44.16 37.27 31.82 27.44 23.86 20.91 18.44 16.36 14.60 13.09 11.78 10.65 9.671 8.810 8.055 7.389 6.800 6.279 5.817 5.406 5.040 4.715 4.426 4.169 3.941 3.739 3.561 3.404 3.267 3.149 3.048 2.962 2.891 2.833 2.789 (continued) 259 260 Appendixes Appendix Continued 0° 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 2.785 2.755 2.736 2.728 2.731 2.745 2.769 2.803 2.848 2.902 2.967 3.042 3.128 3.225 3.333 3.454 3.587 3.733 3.894 4.071 4.265 4.478 4.712 4.970 5.254 5.569 5.919 6.311 6.750 7.247 7.813 8.465 9.222 10.11 11.18 12.48 14.10 16.17 18.93 22.77 28.53 38.11 2.782 2.752 2.734 2.728 2.732 2.747 2.772 2.807 2.853 2.908 2.974 3.050 3.137 3.235 3.345 3.466 3.601 3.749 3.911 4.090 4.285 4.500 4.737 4.997 5.284 5.603 5.957 6.352 6.797 7.300 7.874 8.535 9.305 10.21 11.30 12.63 14.28 16.41 19.25 23.24 29.27 39.43 2.778 2.750 2.733 2.728 2.733 2.749 2.775 2.811 2.858 2.914 2.981 3.059 3.147 3.246 3.356 3.479 3.615 3.764 3.928 4.108 4.306 4.523 4.762 5.024 5.315 5.636 5.994 6.394 6.844 7.354 7.936 8.607 9.389 10.31 11.42 12.77 14.47 16.66 19.59 23.74 30.05 40.84 2.775 2.748 2.732 2.728 2.734 2.751 2.778 2.815 2.863 2.921 2.988 3.067 3.156 3.256 3.368 3.492 3.629 3.780 3.945 4.127 4.327 4.546 4.787 5.052 5.345 5.670 6.032 6.437 6.893 7.409 7.999 8.680 9.474 10.41 11.54 12.93 14.66 16.91 19.94 24.25 30.86 42.36 2.772 2.746 2.731 2.728 2.735 2.753 2.781 2.820 2.868 2.927 2.996 3.075 3.166 3.267 3.380 3.505 3.644 3.796 3.963 4.146 4.348 4.569 4.812 5.080 5.376 5.705 6.071 6.480 6.941 7.464 8.063 8.754 9.561 10.52 11.67 13.08 14.86 17.17 20.30 24.78 31.73 44.00 2.769 2.744 2.730 2.728 2.737 2.755 2.785 2.824 2.874 2.933 3.003 3.084 3.175 3.278 3.392 3.518 3.658 3.812 3.981 4.166 4.369 4.592 4.838 5.108 5.408 5.740 6.109 6.524 6.991 7.521 8.127 8.829 9.649 10.62 11.80 13.24 15.07 17.44 20.68 25.34 32.64 45.76 2.766 2.742 2.730 2.728 2.738 2.758 2.788 2.829 2.879 2.940 3.011 3.092 3.185 3.289 3.404 3.532 3.673 3.828 3.998 4.185 4.390 4.616 4.864 5.137 5.440 5.775 6.149 6.568 7.041 7.578 8.193 8.905 9.739 10.73 11.93 13.41 15.28 17.72 21.07 25.92 33.60 47.68 2.763 2.740 2.729 2.729 2.740 2.761 2.792" 2.833 2.885 2.946 3.019 3.101 3.195 3.300 3.416 3.545 3.688 3.844 4.016 4.205 4.412 4.640 4.890 5.166 5.471 5.810 6.188 6.613 7.091 7.635 8.259 8.983 9.831 10.84 12.06 13.57 15.49 18.01 21.47 26.53 34.63 49.76 2.760 2.739 2.729 2.730 2.741 2.763 2.795 2.838 2.890 2.953 3.026 3.110 3.205 3.311 3.429 3.559 3.703 3.861 4.034 4.225 4.434 4.663 4.916 5.195 5.504 5.846 6.229 6.658 7.142 7.694 8.327 9.061 9.924 10.95 12.20 13.74 15.71 18.31 21.89 27.16 35.72 52.02 2.757 2.737 2.728 2.730 2.743 2.766 2.799 2.843 2.896 2.960 3.034 3.119 3.215 3.322 3.441 3.573 3.718 3.877 4.053 4.245 4.456 4.688 4.943 5.224 5.536 5.883 6.270 6.704 7.194 7.753 8.395 9.141 10.02 11.07 12.34 13.92 15.94 18.61 22.32 27.83 36.88 54.51 Appendixes APPENDIX 8: PHYSICAL CONSTANTS AND CONVERSION FACTORS Physical Constants Avogadro constant Boltzmann constant Charge on electron Planck constant Speed of light Electron mass NA = 6.022 X 1023 particles/mole k = 8.617 X 10-5 eV/K = 1.38 x 10-23 J/K e = 1.602 x 10-19 C h = 4.136 X 10-15 eV· s = 6.626 X 10-34 J C = 2.998 X 108 m/s m = 9.1095 x 10-31 kg Useful Conversion Factors nm = 10-9 m = 10 A = 10-7 em eV = 1.602 x 10-19 J O°C =273 K °C = (OF - 32) x 5/9 K = °C + 273 Prefixes m = milli = 10-3 IJ = micro = 10-6 n = nano = 10-9 P = pico = 10-12 k = kilo = 103 M= mega = 106 G = giga = 109 T = tera = 10 12 S 261 262 Appendixes APPENDIX 9: jCPDS-ICDD CARD NUMBERS FOR SOME COMMON MATERIALS Pearson symbol cPl cP2 cP4 cI2 cF4 cP8 cP12 cF16 hP2 hP4 bRIO Material Card Number a-Po 19-899 CsCI 5-607 Cu)Au 35-1357 Cr 6-694 Ag 4-783 AlN 25-1495 Si 27-1402 CaF2 35-816 Fe)AI 45-1203 Cd 5-674 AlN 25-1133 a-Al2O) 46-1212 AuTel.7 19-528 ~-cuZn 2-1231 Fe 6-696 AI 4-787 CaO 37-1497 TIC 32-1383 Mg 35-821 PTFE 27-1873 FeAl 33-20 'llI 4-788 Au 4-784 GaAs 32-389 TIN 38-1420 W 4-806 Cu 4-836 Ge 4-545 ZnS 5-566 TI 44-1294 Zn Zno Zns 36-1451 36-1450 4-831 Ni 4-850 MgO 45-0946 Pb 4-686 NaCI 5-628 NiO 4-835 Appendixes APPENDIX 10: CRYSTAL STRUCTURES AND LATTICE PARAMETERS OF SOME SELECTED MATERIALS Material a-Alumina Aluminum Aluminum nitride Aluminum nitride j3-Brass Cadmium Calcium oxide Cesium chloride Chromium Copper Copper-gold Calcium fluoride Gallium arsenide Germanium Gold Gold telluride a-Iron Iron aluminide Iron aluminide Lead Magnesium Magnesium oxide Nickel Nickel oxide a-Polonium Silicon Silver Sodium chloride Tantalum Titanium Titanium carbide Titanium nitride Tungsten Zinc Zinc oxide Zinc sulfide Zinc sulfide Symbol a-Al20 AI AlN AlN j3-cuzn Cd CaO CsCI Cr Cu CU3Au CaF2 GaAs Ge Au AuTe!.7 a-Fe FeAl Fe3A1 Pb Mg MgO Ni NiO a-Po Si Ag NaCI Ta Ti TiC TiN W Zn Zno Zns Zns Crystal structure corundum fcc zincblende wurtzite esCI hcp NaCI CsCI bcc fcc simple cubic fluorite zinc blende diamond cubic fcc simple cubic bcc cubic cubic fcc hcp NaCI fcc NaCI simple cubic diamond cubic fcc NaCI bcc hcp NaCI NaCI bcc hcp wurtzite zincblende wurtzite Pearson symbol bRIO cF8 cF8 hP4 cP2 hP2 cF8 cP2 el2 cF4 cP4 cF12 cF8 cF8 cF4 cPl el2 cP2 cF16 cF4 hP2 cF8 cF4 cF8 cPl cF8 cF4 cF8 el2 hP2 cF8 cF8 el2 hP2 hP4 cF8 hP4 Lattice parameters a c cia 0.4759 0.4049 0.4120 0.3111 0.2948 0.2979 0.4811 0.4123 0.2884 0.3615 0.3749 0.5463 0.5654 0.5658 0.4079 0.2961 0.2866 0.2895 0.5793 0.4951 0.3209 0.4211 0.3524 0.4177 0.3359 0.5431 0.4086 0.5640 0.3306 0.2951 0.4327 0.4242 0.3165 0.2665 0.3250 0.5406 0.3821 1.2993 2.7303 0.4979 1.6005 0.5618 1.8857 0.5211 1.6238 0.4683 1.5871 0.4947 0.5207 1.8563 1.6021 0.6257 1.6376 263 Bibliography Classic Books and Historical Perspectives These books are particularly good for students interested in the development and history of the X-ray diffraction technique for characterization of materials Bijvoet, J M., Burgers, W G., and Hiigg G., Eds (1969), Early Papers on Diffraction ofX·RIlys, published for the International Union of Crystallography by N V A Ossthoek's Uitgeversmaatschappij, Utrecht, The Netherlands Some of the classic papers, including those by Max von Laue and W H and w L Bragg, in x·ray diffraction are reprinted in this book Should be of interest to students wanting to know about the history of x-ray diffraction Bragg, W H (1929), An Introduction to Crystal Analysis, Van Nostrand, New York W H Bragg is the fathe!; and this book is based on a series of lectures he gave in 1928 at University College in Aberystwyth Wales Bragg W H., and Bragg W L (1915), X-RilysandCrystaIStructure, G Belland Sons, London, UK The classic book by the Braggs (father and son) This is their first book about x-rays and their use in crystal structure analysis Although it is over 80 years old, it is very readable and the descriptions are clear and concise Bragg, W H., and Bragg, W L., Eds., The Crystalline State, Macmillan, New York Volume I: Bragg W L (1934), A General Survey A clear survey of x-ray diffraction and its use for crystal structure detennination Volume 2: James, R W (1954), The Optical Principles ofthe Diffraction ofX-Rays Advanced theory of x-ray diffraction A mathematical approach only for the very enthusiastic student Volume Lipson H., and Cochran, w (1953), The Determination of Crystal Structures Advanced treatment of structure analysis from a theoretical point of view Ewald, P P., Ed (1962), Fifty Years of X-Ray Diffraction, published for the International Union of Crystallography byN v A Ossthoek's Uitgeversmaatschappij, Utrecht, The Netherlands Provides a very interesting and readable historical perspective of x -ray diffraction Personal reminiscences by some of the big names in the development of the technique are particularly enjoyable 265 266 Bibliography X-Ray Safety As we mentioned in Sec 3.5, commercial x-ray diffractometers are designed to meet extremely stringent safety requirements However, if you want to find out more about the effects of exposure to x-rays, we recommend that you consult the following publications: Henry, H R (1969), Fundamentals ofRAdiation ProtediDn, John Wiley and Sons, New York Lakey, J R A., and Lewins, J D., Eds (1987), AURA Principles, Practice and Consequences, Adam Hilger Bristol UK Proceedings of a conference about the principles of ALARA Principles andApplications ofCollective Dosein RildiationProtection (1995), NCRP Repon No 121, National Council on Radiation Protection and Measurements, Bethesda, MD RAdiation: Doses, Effects, Risks (1985), United Nations Environment Program A shon booklet explaining some of the naturally occurring sources of ionizing radiation and their effects on the human body Crystal Structure To understand the principles of x-ray diffraction, it is important to have at least a basic understanding of crystal structures For the interpretation of x-ray diffraction patterns obtained from crystalline materials, a knowledge of crystal structures is essential To work through the experimental modules and exercises in this book all the information you need to know about crystal structures is provided in Chapter For more information, at the introductory level, most standard undergraduate materials science and engineering textbooks have a chapter on crystal structures For example, we recommend the following textbooks: Callister, W D (1997), Materials Scima and Engineering: An Introduction, 4th ed., John Wiley and Sons, New York Chapter is on the structure of crystalline solids Smith w R (1996), Principles of Materials Scima and Engineering, 3rd ed., McGraw-Hill, New York Chapter is on crystal structure and crystal geometry At a more advanced level you may find the following books useful: Barrett C S., and Massalski T B (1980), The Strudure ofMetals, 3rd ed., McGraw-Hill New York A classic book dealing with the structures of metals and structural characterization by x -ray diffraction Kingery, W D., Bowen, H K., and Uhlmann, D R (1976), Introduction to Ceramic;, 2nd ed., John Wiley and Sons, New York Chapter is an overview of the structures of ceramic materials Pearson, W B (1972), The Crystal Chemistry and Physia ofMetals and Alloys, John WJ!ey and Sons, New York Includes notation for crystal structures including Pearson symbols that we have used in our book Also discusses crystal structures Bibliography X-Ray Diffraction The technique of x-ray diffraction has been the subject of many books_ Here are some that we found useful when we were learning the technique: Azaroff, L V (1968), Elements ofX-Ray Crystallo9raphy, McGraw-Hill, New York Provides a fundamental understanding of the basic principles of x-ray diffraction Emphasizes the reciprocal lattice concept Most useful for a course in physics rather than materials science Azaroff, L v., and Buerger, M J (1958), The Powder Method in X-Ray Crystall09raphy, McGraw-Hill, New York One of the early books on recording and interpreting x-ray powder patterns Barrett, C S., and Massalski, T_ B (1980), The Structure ofMetals, 3rd ed., McGraw-Hill, New York A classic book dealing with the structures of metals and structural characterization by x-ray diffraction Cullity, B D (1978), Elements of X-Ray Diffraction, 2nd ed., Addison-Wesley, Reading MA An introduction to x-ray diffraction The background information on structures and symmetry makes it suitable for undergraduates and first-year graduate students in materials science Guinier, A (1963), X-Ray Diffraction, W H Freeman, San Francisco, CA A comprehensive book dealing with the x-ray diffraction of crystals, imperfect crystals, and amorphous solids Determination of crystal structures is not covered Klug, H P., and Alexander L E (1974), X-Ray Diffraction Procedures, 2nd ed., John Wiley and Sons, New York A very comprehensive textbook dealing with many aspects of powder diffraction (both theory and practice) Mclachlan, Jr., D (1957), X-Ray Crystal Structure, McGraw-Hill, New York A book more useful to physics graduate students or to those whose interests lie more in crystallography Nuffield, E W (1966), X-Ray Diffraction Methods, John Wiley and Sons, New York A book dealing with all methods of x-ray diffraction, particularly directed at students in the earth sciences Schwartz, L H., and Cohen, J B (1977), Diffraction from Materials, 2nd ed., Academic Press, New York Covers not only x-ray diffraction but also electron and neutron diffraction Stout, G H., and Jensen, L H (1968), X-Ray Structure Determination, Macmillan, New York An advanced book dealing with practical problems of solving crystal structures through x-ray diffraction Warren, B E (1969), X-Ray Diffraction, Addison-Wesley, Reading, MA This is an excellent advanced textbook useful to graduate students in materials science and physics The treatment of the subject is theoretical and therefore may be a bit heavy for undergraduate students Woolfson, M M (1977), An Introduction to X-ray Crystallo9raphy, 2nd ed., Cambridge University Press, Cambridge, UK A good book on crystallography and experimental details of recording x-ray diffraction patterns Also lists computer programs to calculate structure factors, electron density maps, anomalous scattering, and solution of crystal structures 267 268 Bibliography WooHson, M M., and Fan, H-F (1995), Physical and Non-Physical Methods ofSolvins Crysfill Structures, Cambridge University Press, Cambridge, UK A comprehensive book on the theory of solving crystal structures Data Books and Resources for Crystallographic Information Here are some of the sources of information you might find useful when trying to index an x-ray diffraction pattern or to identify a material Ca.R.lne Crystallosraphy 3.0, Distributed by ESM Software, 2234 Wade Court, Hamilton, OH 45013; leI: 513-738-4773; FAX: 513-738-4407 Software programs to generate real lattices in 3D, reciprocal lattices in 3D and 2D, stereographic projections, and ideal diffraction patterns (peak positions and intensities) For a free demonstration of the software you can go to the following web site on the internet: http://www.lmcp.jussieu.frlsincris/logiciellcarine/ Donnay, J D H., Donnay, G., Cox, E G., Kellllllld, 0., and Vernon, M (1963), Crystal Data Determinative Tables, 2nd ed., The American Crystallographic Association, Washington Crystallographic data on many compounds Fang J H., and Bloss, R D (1966), X-Ray Diffraction Tables, Southern Dlinois University Press, Carbondale, ll Tables of interplanar spacings (d) corresponding to 29 for various wavelengths This information can now be obtained using most software packages available with modem x-ray diffractometers Lide, D R., Ed (1996-1997), CRC Handbook of Chemistry and Physics, 77th ed., CRC Press, Boca Raton, FL Often one of the first sources you should try when you want information about a material Massalski, T B., Ed (1990), Binary Alloy Phase Diasrams, 2nd ed., ASM International, Materials Park OH Volume 1: Ac-Ag to Ca-Zn; Volume 2: Cd-Ce to Hf-Rb; Volume 3: Hf-Re to Zn-Zr The standard reference source for phase diagrams of alloys Pearson, W B., A Handbook of Lattice Spacings and Structures of Metals and Alloys, Vol (1958), Vol (1967), Pergamon Press, Oxford, UK Lists lattice spacings of alloys and compounds as a function of solute content Phase Diasrams for Ceramists, The American Ceramic Society, columbus, OH Volume 1: Levin, E M., Robbins, C R., and McMurdie, H F., Eds (1964) Volume 2: Levin, E M., Robbins, C R., and McMurdie, H F., Eds (1969) Volume 3: Levin, E M., and McMurdie, H R, Eds (1975) Volume 4: Roth R S., Negas, T., and Cook L P., Eds (1981) Volume 5: Roth R S., Negas, T., and Cook L P., Eds (1983) The standard reference source for phase diagrams of ceramics Powder Diffraction File, 1norsanic Phases Search Manual (Hanawalt), International Centre for Diffraction Data, Swarthmore, PA Tabulation of peak positions and intensities for inorganic materials Essential for identification of unknown materials by x-ray diffraction An updated volume is published each year Villars, P., and Calvert, L D (1991), Pearson's Handbook ofCrystallosraphic Data for Intennetallic Phases (in four volumes), ASM International, Materials Park OH Crystallographic information on pure metals, semiconductors, and ceramic compounds, in addition to intermetallic phases Bibliography Wilson, A J C., Ed (1995), InternatiolUll Tables/orCrysUlllography, Vol c., Mathematical, Physical and Chemical Tables, Kluwer Academic Publishers, Dorcirecht, The Netherlands Covers many aspects of diffraction, including x-ray diffraction, and provides a comprehensive list of data on characteristic wavelengths, absorption coefficients, atomic scattering factors, etc An invaluable reference wyckoff R w G (1963), CrysUlI Structures, 2nd ed., John Wiley and Sons, New York Describes many crystal structures 269 Index Complex exponential functions, 55 Constructive interference, 18 Continuous spectrutn, Crystal monochromators, 70 Crystal structure, 27 notation for, 41 of some compounds, table, 35, 263 Crystal structure determination cubic structures, 97 hexagonal structures, 125 Crystal systems, 24 table, 25 Crystallite size, determination of, 207 CsCI structure, 36 Absorption, 66 of x-rays, 12 Absorption coefficients, linear, 224 mass, 224 table, 257 ALARA, principles, 92 Amorphous solids, 21 Angstom unit, ASTM, grain size charts, 210 Atomic packing factor (APF), 31 Atomic scattering factor, 17 table, 255 Background radiation, 81 Basis, 27 Body-centered cubic structure, 28 Body-centering translation, 28 Bragg's law; 50 Bravais lattices, 24 Debye-Scherrer camera, 156 errors, 156 Debye-Scherrer method, 166 Densities, table, 257 Destructive interference, 18 Detectors, 72 energy resolution, 76 proportional, 73 position sensitive, 74 scintillation, 74 solid state, 75 Diamond cubic structure, 33 Diffraction, 14 from amorphous materials, 60 comparison with reflection, 50 from crystalline materials, 50 Diffraction pattern, standard features, 80 aluminum, 81,82, 102, 162,217 aluminum nitride, 146 C60 structure, 41 Cauchy profile, 211 Cell volumes, equations, 252 Centering translations, 28, 30 Cesium chloride structure, 36 Characteristic radiation, wavelength, table, 14 Chemical analysis by diffraction, 237 single-phase material, 240 two-phase materiaL 243 Cohen's method, 159 Coherent scattering, 15 Cold-worked metaL 209 Collimators, 71 271 272 Index Diffraction pattern (cont.) aluminum-silicon powder mixture, 231 chromium, 106 cold-worked aluminum 216 cold-worked copper, 216 copper, 108,219 copper-gold fully disordered 201 copper-gold partially ordered, 202 cubic materials, 83 iron, 110 magnesium, 135 magnesium oxide, 179 magnesium oxide-calcium oxide mixture, 233 magnesium oxide-nickel oxide alloys, 181 183, 185, 187 nickel 112 nickel oxide, 189 silicon 114 titanium 141 titanium nitride, 118 zinc, 130 Diffractometer errors, 157 general features, 63 optics, 68 specimen preparation 66 Disappearing phase method 175 Domains, 209 Elastic scattering 15 Electromagnetic spectrum, Electron transitions, selection rules for, 13 Electron volt, Escape peak, 80 Extrapolation functions, 156 Face-centered cubic structure, 29 Face-centering translations, 30 Fluorescence, 74 Fluorescent radiation, 65 Fluorite structure, 40 Fundamental reflections, 198 Gaussian profile, 211 Germanium detector, 79 Glasses, 61 Grain boundaries, 22 Hanawalt method, 87, 239 Hexagonal close-packed structure, 31 Hull-Davey chart, 126 ICDD (International Centre for Diffraction Data),86 Indexing powder patterns, cubic crystals, 97 hexagonal crystals, 125 Indices, of directions, 47, 49 of planes, 43 Inelastic scattering 15 Integrated intensity, 59, 69 Intensities of peaks, 59, 224 Interference, 16 JCPDS (Joint Committee on Powder Diffraction Standards), 86 card numbers, 262 Lattice, 23 points per cell 25 Lattice parameters, 23 table, 263 converting between hexagonal and facecentered cubic lattices, 177 Lattice-parameter measurements, cubic structures, 100 hexagonal structures, 128 precise measurements, 154 Lattice strain determination of, 207 Least squares, method of, 160 Lever rule, 170 linear absorption coefficient, 224 Long-range order, 21 detection of, 193 Long-range order parameter, 194 Lorentz-polarization factor 58 table, 259 Lorentzian profile, 211 Mass absorption coefficient, 224 table, 257 Miller-Bravais indices, 48 Miller indices, 43 quadratic forms, table, 254 Monochromators, 70 Multiplicity factor, 45 table, 258 NaCi structure, 37 Nonprimitive cells, 25 Order, long-range, 21 parameter, 194 short-range, 22 Order-disorder transformations, 194 in Ii-brass, 203 Index Order-disorder transfonnations (cont.) in copper-gold 195 in copper-palladium, 203 in copper-platinum, 203 in iron-aluminum, 203 Parametric method 174 Peak broadening, due to crystallite size, 208 faulting, 209 instrumental effects, 208 strain,208 Pearson symbols, 41 for some crystal structures, 42 table, 42 Peltier effect, 79 phase diagrams, detennination of, 167 gennanium-silicon, 168 gold-copper, 195 magnesium oxide-calcium oxide, 168 titanium-aluminum, 169 Physical constants, table, 261 Planar density, 47 Plane-spacing equations, table, 251 Point lattice, 23 Polymers, 62 Polymorphism, 35 Position-sensitive detector 74 Powder diffraction file (PDF), 85, 238 Powder mixtures, quantitative analysis of, 223 direct comparison method, 227 external standard method, 226 internal standard method, 228 Precise lattice parameter measurements, 153 Preferred orientation, 67 Primitive cells, 25 Proportional detector, 73 Quadratic fonns of Miller Indices, table, 254 Quantum numbers, 10 Radiation dose, unit of, 92 Rock-salt structure, 35 Safety precautions, 91 Scattering, 14 Scherrer fonnula, 212 Scintillation detector, 74 Selection rules, 54; see also Structure factor cubic materials, table, 99 table, 59 Short-range order, 22 Short-wavelength limit, Si(U) detector, 75 Simple cubic structure, 28 Sodium chloride structure, 37 Solid solubility, determination, 176 substitutional, Hume-Rothery rules for, 175 Solid state detector, 75 Soller slits, 68 Spinel structure, 41 Structure factor, 52 for diamond cubic structure, 57 for fcc structure, 55 for NaCl structure, 56 for simple cubic structure, 55 table, 59, 256 Subgrain structure, 209 Superlattice reflections, 198 Superposition of waves, 16 Temperature factor, 60 Texture, 67 Unit cell, 23 unit-cell volume equations, 252 Unknown material, identification of, 237 single-phase material, 240 two-phase material, 243 Vegard's law, 177 Wavelengths, of commonly used X-rays, table, 14 critical absorption wavelength, 12 Weighted average, 11 X-ray camera, 156,210 X-ray tubes, X-rays, absorption of, 12 characteristic, continuous, detection of, 72 fluorescent, 65 production of, safety precautions, 91 ZnS (zinc blende structure), 38 273